I've read that squats and deadlifts promote overall muscle growth in the body. Does this mean that if I want to increase growth faster in, say, my arms, I should exercise my arms on the same day as I do one of these heavy compound lifts?
I like the tree analogy. Spot on. There is no right or wrong answer. Everyone has their own way. Some work better then others. I train arms with legs. Sort of an upper lower. I also do a push pull routine. Change my routine every two months. I go heavy on compound movements then meduim to light on isolation movements such as arm work etc. just work hard not too long and use good form and things will be fine. Some parts can be stubborn for growth. Experiment with reason
Squats and deadlifts definitely promote growth. But that is not the whole story.
I use the tree analogy. You don't see a tree with a tiny trunk and big thick branches. If you want the thick branches you have to have a thicker trunk.
So yes doing squats and deadlifts will promote complete body strength but that isn't the whole story.
Thing #1 - So you are starting out and want to get big quick. Yes go heavy on squats and deadlifts. But you have to do some arms. First you need a little triceps to help bench. Second the arm workouts help forearm and hand strength which help deadlifting and other lifts. Then the biggest thing is so where are you at after 6-12 months of deadlifting and squatting when you have got a little bigger and you haven't touched your arms? Well you are starting your arm workout and your arms will basically be shocked for a while. Why not work them out (even marginally) so that your body can adjust easier to new routines?
Thing #2 - You might be at a point where you are not going to have huge gains in deadlifts and squats. Of course working out your arms hard will make them stronger and bigger. I don't think we need to debate that working out a body part makes it stronger/bigger.
Thing #3 - If you want size you need intensity for the reps or weight. You can't do everything with intensity. You get about 30 mins if you are lucky with high intensity. So you if you want great arms you need to do them on their own.
There is no reason not to do them on the same day. The key is to not overdo the load. In short no more than 5 sets of 5 reps on squats and 1 set of 5 reps on the deadlift. BTW, deadlift is probably the best exercise to improve your grip.
My background is strength training, so my answer may not exactly be what you are looking for. Essentially for strength gains squats and deadlifts are excellent exercises. My program alternates two full body workouts with a day of rest in between. Squats are done every session. The upper body swaps between bench press and overhead press. The other exercise swaps between barbell rows and deadlifts (both get the back muscles).
Incorporating squats and deadlifts into a split routine is very tricky precisely because they hit so many areas on your body.
You have to factor in recovery time, which really depends on how much volume you are doing, and your ability to recover. A beginner recovers pretty quickly, but that is because they can't get the same volume as a very strong intermediate lifter (someone who can squat 1.5x body weight to full parallel).
Lastly, you have to make sure you do these lifts correctly or you will get injured. If you do half squats or anything less than the full range of motion (ROM) you are setting yourself up for injury at a later point. If you don't perform the steps of the deadlift correctly you can injure your back. Yet, they are very powerful lifts. Even if it's not your goal, you won't be able to help getting stronger doing these lifts.
Your program can work as long as you have a full day of rest between each workout. Other than your forearms, neither lift works the arms appreciably.
NOTE: regarding the question of them stimulating arm growth, I don't think that they do. Your muscles respond to stress that you put on them, and neither lift stresses the arms that much.
An Example: 1. Chest - Shoulders
Great bi busters - 21's - get a medium/light weight barbell and do standing curls - 7 reps that go from bottom to halfway point then without rest or putting dumbbell down do 7 reps from top to the halfway down point then without rest or putting dumbbell down do 7 full range reps! I usually do 3-5 sets of these and call it a day!
Another fav is get three sets of dumbbells 10-15-20 and do super sets - 1x10 w/10lb then without rest 1x10 w/15lb - then without rest 1x10 w/20lb - I usually do 3-5 sets of these and call it a day!
On last recommendation for overall arm size...DIPS, DIPS and more DIPS!